Basically a dialysis machine includes two fluid systems (fluid circuits), i.e. the so called extracorporeal blood conduit system, also referred to as external fluidics in the present application, and the so called dialysis fluid system, also referred to as internal fluidics, arranged inside the machine (as part of the machine). The extracorporeal blood conduit system and the internal fluidics are in (mass exchange) communication via the dialyzer and the membrane thereof. The extracorporeal blood conduit system is connected via an arterial access and a venous access to the intracorporeal blood circuit of a patient. From the internal fluidics physiological fluid, especially dialysis fluid, can be supplied to the extracorporeal blood conduit system, e.g. for re-supplying large fluid quantities which are deliberately withdrawn from the patient during a dialysis treatment.